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DOE OSTI2021

HIBP Applications to Advance Understanding of Plasma Transport Physics (2011-2017) (and subsequently titled) Development of Beam Measurements to Advance Understanding of Transients and Improve Validation (2017-2020) (Final Technical Report)

This is the Final Technical Report for the DoE Measurement Innovation (previously Diagnostic Development) grant DE-SC0006077 titled HIBP Applications to Advance Understanding of Plasma Transport Physics (2011-2017), and subsequently titled Development of Beam Measurements to Advance Understanding of Transients and Improve Validation (2017-2020). The grant was funded by the Office of Fusion Energy Sciences (FES) for the period 1 May 2011–17 July 2020. Work performed through the grant has resulted in diagnostic innovations and new measurement capabilities that will improve understanding of transport, magnetic equilibrium, and electric fields in magnetically confined plasmas. We have developed novel hardware and advanced techniques to expand beam-based diagnostic capabilities, and extend measurements to new operating regimes. Some have been realized using a Heavy Ion Beam Probe (HIBP) having traditional features, while other applications have joined our innovations with subsets of advantageous HIBP features. This work has established smaller, more economical detection systems and, in doing so, may enable substantial extension of scenarios in which beam-based diagnostics are deployed. Key Measurement Innovations include: Computer Models and Simulations of HIBP Applications-Computer modeling and simulating of HIBP applications is central to predicting interaction of beam particles with plasmas, designing diagnostic systems, and anticipating measurement characteristics. We have extended the capability and improved measurement fidelity of the HIBP diagnostic on the Madison Symmetric Torus (MST) reversed field pinch (RFP); simulated feasibility of HIBP operation in the Helically Symmetric eXperiment (HSX) optimized stellarator; and investigated the plausibility of HIBP measurements in the ASDEX Upgrade tokamak. We have also developed a new technique that uses ion optics to model a finite phase-space beam. It yields more realistic (than traditional method) estimates of sample volume characteristics, which influence measurement resolution and sensitivity. Extension of Diagnostic Capabilities and Measurements on the MST RFP-Capabilities have been extended using the first and only HIBP installation on an RFP. Challenges associated with operation of the diagnostic on MST include the three-dimensional nature of particle trajectories, temporal topology and amplitude changes in the plasma equilibrium, and strong particle and radiative emission from the plasma. We have addressed these challenges through development of detailed and higher precision diagnostic simulations, calibrated subtraction of noise to resolve secondary ion signals, and implementation of hardware that enables higher fidelity measurement of plasma fluctuations. Development of New Hardware and Measurement Techniques - We have advanced beam-based measurement capabilities via development of new detectors and techniques to determine the poloidal magnetic flux ψ in the plasma, and enable placement of detectors close to the plasma and thus allow a smaller and less expensive diagnostic. We have demonstrated measurement of ψ, an ability that was made possible by development of highly effective noise reduction techniques. We also modeled the effect of non-ideal and instrumentation effects by developing a virtual (simulated) diagnostic. Application of beam-based diagnostics on various devices and multiple magnetic configurations (e.g. stellarator, tokamak, and reversed field pinch) enables investigation of critical physics issues and measurements resulting in the broad parameter space data needed to test and validate theory & modeling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

ARQUIN: Architectures for Multinode Superconducting Quantum Computers

Many proposals to scale quantum technology rely on modular or distributed designs wherein individual quantum processors, called nodes, are linked together to form one large multinode quantum computer (MNQC). One scalable method to construct an MNQC is using superconducting quantum systems with optical interconnects. However, internode gates in these systems may be two to three orders of magnitude noisier and slower than local operations. Surmounting the limitations of internode gates will require improvements in entanglement generation, use of entanglement distillation, and optimized software and compilers. Still, it remains unclear what performance is possible with current hardware and what performance algorithms require. In this article, we employ a systems analysis approach to quantify overall MNQC performance in terms of hardware models of internode links, entanglement distillation, and local architecture. We show how to navigate tradeoffs in entanglement generation and distillation in the context of algorithm performance, lay out how compilers and software should balance between local and internode gates, and discuss when noisy quantum internode links have an advantage over purely classical links. Here, we find that a factor of 10–100× better link performance is required and introduce a research roadmap for the co-design of hardware and software towards the realization of early MNQCs. While we focus on superconducting devices with optical interconnects, our approach is general across MNQC implementations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

HPC Resource Allocation Under Energy Constraints

We discuss the new problem faced by High-Performance Computing (HPC) facilities in allocating resources to users of their facilities: while facilities once allocated a single finite resource—node-hours—now facilities must also concurrently allocate a second scarce resource: electrical energy, which is bounded within each facility's annual operations budget. Current application optimization practices encourage conservation of the first resource, but can be potentially unaffordably wasteful of the second. We describe a framework for reasoning about such allocations that can be utilized by facilities to articulate policy, while encouraging scientific application developers to write code mindfully of both constraints. We outline the requirements on facilities, on developers, and on hardware vendors and integrators that are necessary to enable the implementation of this framework.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Hardware-in-the-Loop (HIL) Simulations for Smart Grid Impact Studies

Hardware-in-the-loop (HIL) simulations are increasingly employed in power engineering as more inverter-based generation and smart appliances are connected to the electric grid. HIL techniques allow for the co-simulation of analytical models with actual devices whose complex behavior is computationally inefficient or difficult to model. They also allow for testing the behavior of these devices under adverse conditions that rarely occur in the field but are important to evaluate. This paper provides an overview of how HIL simulations have been used to date and proposes that HIL simulations should play an important role in evaluating new control strategies, especially at the distribution level, that are being proposed to allow for continued affordable and reliable operation of the electric grid. We present a new capability that was developed to evaluate the interactions between residential loads and the smart grid: smart home hardware-in-the-loop. The paper includes results from an HIL experiment that incorporates multiple technologies and controls.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Universal Compiling and (No-)Free-Lunch Theorems for Continuous-Variable Quantum Learning

Quantum compiling, where a parameterized quantum circuit is trained to learn a target unitary, is an important primitive for quantum computing that can be used as a subroutine to obtain optimal circuits or as a tomographic tool to study the dynamics of an experimental system. While much attention has been paid to quantum compiling on discrete-variable hardware, less has been paid to compiling in the continuous-variable paradigm. Here we motivate several, closely related, short-depth continuous-variable algorithms for quantum compilation. We analyze the trainability of our proposed cost functions and numerically demonstrate our algorithms by learning arbitrary Gaussian operations and Kerr nonlinearities. We further make connections between this framework and quantum learning theory in the continuous-variable setting by deriving no-free-lunch theorems. These generalization bounds demonstrate a linear resource reduction for learning Gaussian unitaries using entangled coherent-Fock states and an exponential resource reduction for learning arbitrary unitaries using two-mode-squeezed states.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

SYMBIOSYS: A Methodology for Performance Analysis of Composable HPC Data Services

Microservices are a powerful new way of building, customizing, and deploying distributed services owing to their flexibility and maintainability. Several large-scale distributed platforms have emerged to serve the growing needs of data-centric workloads and services in commercial computing. Concurrently, high-performance computing (HPC) systems and software are rapidly evolving to meet the demands of diversified applications and heterogeneity. The interplay of hardware factors, software configuration parameters, and the flexibility offered with a microservice architecture makes it nontrivial to estimate the optimal service instantiation for a given application workload. Further, this problem is exacerbated when considering that these services operate in a dynamic and heterogeneous HPC environment. An optimally integrated service can be vastly more performant than a haphazardly integrated one. Existing performance tools for HPC either fail to understand the request-response model of communication inherent to microservices or they operate within a narrow scope, limiting the insight that can be gleaned from employing them in isolation. We propose a methodology for integrated performance analysis of HPC microservices frameworks and applications called SYMBIOSYS. We describe its design and implementation within the context of the Mochi framework. This integration is achieved by combining distributed callpath profiling and tracing with a performance data exchange strategy that collects fine-grained, low-level metrics from the RPC communication library and network layers. The result is a portable, low-overhead performance analysis setup that provides a holistic profile of the dependencies among microservices and how they interact with the Mochi RPC software stack. Using HEPnOS, a production-quality Mochi data service, we demonstrate the low-overhead operation of SYMBIOSYS at scale and use it to identify the root causes of poorly performing service configurations.

microservices↗

DOE OSTI2020

Virtualized Logical Qubits: A 2.5D Architecture for Error-Corrected Quantum Computing

Current, near-term quantum devices have shown great progress in the last several years culminating recently with a demonstration of quantum supremacy. In the medium-term, however, quantum machines will need to transition to greater reliability through error correction, likely through promising techniques like surface codes which are well suited for near-term devices with limited qubit connectivity. We discover quantum memory, particularly resonant cavities with transmon qubits arranged in a 2.5D architecture, can efficiently implement surface codes with substantial hardware savings and performance/fidelity gains. Specifically, we virtualize logical qubits by storing them in layers of qubit memories connected to each transmon. Surprisingly, distributing each logical qubit across many memories has a minimal impact on fault tolerance and results in substantially more efficient operations. Our design permits fast transversal application of CNOT operations between logical qubits sharing the same physical address (same set of cavities) which are 6x faster than standard lattice surgery CNOTs. We develop a novel embedding which saves approximately 10x in transmons with another 2x savings from an additional optimization for compactness. Although qubit virtualization pays a 10x penalty in serialization, advantages in the transversal CNOT and in area efficiency result in fault-tolerance and performance comparable to conventional 2D transmon-only architectures. Our simulations show our system can achieve fault tolerance comparable to conventional two-dimensional grids while saving substantial hardware. Furthermore, our architecture can produce magic states at 1.22x the baseline rate given a fixed number of transmon qubits. Here, this is a critical benchmark for future fault-tolerant quantum computers as magic states are essential and machines will spend the majority of their resources continuously producing them. This architecture substantially reduces the hardware requirements for fault-tolerant quantum computing and puts within reach a proof-of-concept experimental demonstration of around 10 logical qubits, requiring only 11 transmons and 9 attached cavities in total.

quantum computing↗

DOE OSTI2024

Development of Real-Time High-Density Pulsar Data Transmission and Processing for Grid Synchronization

Taking advantage of the extreme stability of the pulsar period, it can serve as the timing source for grid synchronization to compensate for the timing drift instigated by the loss of GPS signal. Nevertheless, the real-time transmission and processing of the pulsar data suffer from its high-frequency data rate, varying from megahertz to gigahertz, resulting in reduced computing speed and increased time delay. To mitigate this issue, the hardware and software frameworks are implemented for the high-density pulsar data transmission and processing for grid synchronization in this research. Initially, the high-density pulsar data is transferred using open-source software. The complementary duty cycle timing module is designed to coordinate the operation of the dual-channel high-speed interface and software. Subsequently, the multiple-threading is applied to the receiving, parsing, and splicing pulsar data. Next, the pulsar signal extraction method is implemented based on the polyphase filterbank and time of arrival estimation. Ultimately, real-time performance verification experiments are carried out for different components under two hardware platforms. Finally, the results demonstrate that only 0.482 s is required for processing 4 Gigabyte data through multiple-threading, which is 3.8 times faster than the single thread. The pulsar signal extraction can also be executed within 707 ms for 4.8 seconds of data, thereby indicating that real-time requirements can be met.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

ARCH Technology Snapshot Autonomous Robot Control Hierarchy (ARCH): A universal software system that removes the need to rebuild robotic software for every new platform or task

Robots are increasingly used to perform repetitive, hazardous, and time-sensitive tasks, improving safety and operational efficiency. However, most robotic systems remain difficult to adapt because they are tightly tied to specific hardware and require extensive reprogramming for each new configuration.

42 ENGINEERING↗

DOE OSTI2017

Mapping of exhaust gas recirculation and combustion-residual backflow in the intake ports of a heavy-duty diesel engine using a multiplexed multi-species absorption spectroscopy sensor [Mapping of EGR and combustion residual backflow in the intake ports of a heavy duty diesel engine using a multiplexed multi-species absorption spectroscopy sensor]

Here, the combustion-residual backflow into the intake ports of a commercial diesel engine (Cummins ISX series) was spatiotemporally mapped using a multiplexed multi-species absorption spectroscopy sensor system; the resulting cycle- and cylinder-resolved measurements are applicable for assessing cylinder charge uniformity, control strategies, and computational fluid dynamics tools. On-engine measurements were made using four compact (3/8 in Outside Diameter) stainless steel probes which enabled simultaneous multi-point measurements, required minimal engine hardware modification, and featured a novel tip design for measurement of gas flows parallel to the probe axis. Three sensor probes were used to perform simultaneous backflow measurements in intake runners corresponding to three of the six engine cylinders, and a fourth probe was installed in the intake manifold plenum for tracking dynamics introduced by an external exhaust gas recirculation mixer. Near-crank-angle resolved measurements (5 kHz, that is, 1.2 crank angle resolution at 1000 RPM) were performed during steady-state engine operation at various levels of external exhaust gas recirculation to measure the gas properties and penetration distance of the backflow into the intake runners on a cylinder- and cycle-basis. Validation of computational fluid dynamics model results is also presented to demonstrate the utility of such measurements in advancing engine research.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2019

Nanosystems, Edge Computing, and the Next Generation Computing Systems

It is widely recognized that nanoscience and nanotechnology and their subfields, such as nanophotonics, nanoelectronics, and nanomechanics, have had a tremendous impact on recent advances in sensing, imaging, and communication, with notable developments, including novel transistors and processor architectures. For example, in addition to being supremely fast, optical and photonic components and devices are capable of operating across multiple orders of magnitude length, power, and spectral scales, encompassing the range from macroscopic device sizes and kW energies to atomic domains and single-photon energies. The extreme versatility of the associated electromagnetic phenomena and applications, both classical and quantum, are therefore highly appealing to the rapidly evolving computing and communication realms, where innovations in both hardware and software are necessary to meet the growing speed and memory requirements. Development of all-optical components, photonic chips, interconnects, and processors will bring the speed of light, photon coherence properties, field confinement and enhancement, information-carrying capacity, and the broad spectrum of light into the high-performance computing, the internet of things, and industries related to cloud, fog, and recently edge computing. Conversely, owing to their extraordinary properties, 0D, 1D, and 2D materials are being explored as a physical basis for the next generation of logic components and processors. Carbon nanotubes, for example, have been recently used to create a new processor beyond proof of principle. These developments, in conjunction with neuromorphic and quantum computing, are envisioned to maintain the growth of computing power beyond the projected plateau for silicon technology. We survey the qualitative figures of merit of technologies of current interest for the next generation computing with an emphasis on edge computing.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Numerical Methodology for Optimization of Compression-Ignited Engines Considering Combustion Noise Control

It is challenging to develop highly efficient and clean engines while meeting user expectations in terms of performance, comfort, and drivability. One of the critical aspects in this regard is combustion noise control. Combustion noise accounts for about 40 percent of the overall engine noise in typical turbocharged diesel engines. The experimental investigation of noise generation is difficult due to its inherent complexity and measurement limitations. Therefore, it is important to develop efficient numerical strategies in order to gain a better understanding of the combustion noise mechanisms. In this work, a novel methodology was developed, combining computational fluid dynamics (CFD) modeling and genetic algorithm (GA) technique to optimize the combustion system hardware design of a high-speed direct injection (HSDI) diesel engine, with respect to various emissions and performance targets including combustion noise. The CFD model was specifically set up to reproduce the unsteady pressure field inside the combustion chamber, thereby allowing an accurate prediction of the acoustic response of the combustion phenomena. The model was validated by simulating several steady operating conditions and comparing the numerical results against experimental data, in both temporal and frequency domains. Thereafter, a GA optimization was performed with the goal of minimizing indicated specific fuel consumption (ISFC) and combustion noise, while restricting pollutant (soot and NOx) emissions to their respective baseline values. Eight design variables were selected pertaining to piston bowl geometry, nozzle inclusion angle, number of injector nozzle holes, and in-cylinder swirl. An objective merit function (MF) based on the emissions, ISFC, and combustion noise was constructed to quantify the strength of the engine designs and was determined using the CFD model as the function evaluator. The in-cylinder noise level was characterized by the total resonance energy of local pressure oscillations. The optimum engine configuration thus obtained showed a significant improvement in terms of efficiency and combustion noise compared to the baseline system, along with both soot and NOx emissions within their respective constraints. This optimum configuration included a deeper and tighter bowl geometry with higher swirl and larger number of nozzle holes. Subsequently, a more detailed acoustics analysis based on proper orthogonal decomposition (POD) technique was carried out to further explore the combustion noise benefits achieved by the GA optimum. In conclusion, this computational study is a first of its kind (to the best of the authors’ knowledge), which demonstrates a comprehensive framework to incorporate combustion noise into a numerical optimization strategy for engine design.

42 ENGINEERING↗

DOE OSTI2023

Design and implementation of I/O performance prediction scheme on HPC systems through large-scale log analysis

Abstract Large-scale high performance computing (HPC) systems typically consist of many thousands of CPUs and storage units used by hundreds to thousands of users simultaneously. Applications from large numbers of users have diverse characteristics, such as varying computation, communication, memory, and I/O intensity. A good understanding of the performance characteristics of each user application is important for job scheduling and resource provisioning. Among these performance characteristics, I/O performance is becoming increasingly important as data sizes rapidly increase and large-scale applications, such as simulation and model training, are widely adopted. However, predicting I/O performance is difficult because I/O systems are shared among all users and involve many layers of software and hardware stack, including the application, network interconnect, operating system, file system, and storage devices. Furthermore, updates to these layers and changes in system management policy can significantly alter the I/O behavior of applications and the entire system. To improve the prediction of the I/O performance on HPC systems, we propose integrating information from several different system logs and developing a regression-based approach to predict the I/O performance. Our proposed scheme can dynamically select the most relevant features from the log entries using various feature selection algorithms and scoring functions, and can automatically select the regression algorithm with the best accuracy for the prediction task. The evaluation results show that our proposed scheme can predict the write performance with up to 90% prediction accuracy and the read performance with up to 99% prediction accuracy using the real logs from the Cori supercomputer system at NERSC.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Hardware-in-the-Loop (HIL) Simulations for Smart Grid Impact Studies: Preprint

Hardware-in-the-loop (HIL) simulation is increasingly employed in power engineering as more inverter-based generation and smart appliances are connected to the electric grid. HIL techniques allow for co-simulation of analytical models with actual devices whose complex behavior is computationally inefficient or difficult to capture. It also allows for testing of the behavior of these devices under adverse conditions that only occur rarely in the field, but that are important to evaluate. An overview of how HIL simulation has been used to date is provided. This paper further proposes that HIL simulation should play an important role in evaluating new control strategies, especially at the distribution level, that are being proposed to allow for continued affordable and reliable operation of the electric grid with the introduction of these new technologies. It presents a new capability that was developed to enable evaluation of interactions between residential loads and the smart grid: smart home hardware-in-the-loop. The paper includes results from an HIL simulation that incorporates multiple technologies and controls.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

SpecFIDLER User Manual (Software V.2.5.0)

The Spectroscopic Field Instrument for Detection of Low Energy Radiation (SpecFIDLER) allows response teams to detect and quantify plutonium contamination on the ground. Notional scenarios include dispersion from a weapon accident, or the launch failure of a space probe containing a radioisotope thermoelectric generator. Unlike other instruments, the thin-window sodium iodide detector is sensitive to the low-energy gamma rays emitted by plutonium isotopes. The system supports both mobile survey as well as stationary sampling. This manual provides information about installing, maintaining, and troubleshooting the SpecFIDLER. The scope of this document includes the physical hardware, software for data acquisition, and algorithms for data analysis. Recent changes to the software and algorithms aim to streamline the operation of the system.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

SpecFIDLER User Manual (Software V.2.6.0)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2016

An efficient and portable SIMD algorithm for charge/current deposition in Particle-In-Cell codes

In current computer architectures, data movement (from die to network) is by far the most energy consuming part of an algorithm (≈20pJ/word on-die to ≈10,000 pJ/word on the network). To increase memory locality at the hardware level and reduce energy consumption related to data movement, future exascale computers tend to use many-core processors on each compute nodes that will have a reduced clock speed to allow for efficient cooling. To compensate for frequency decrease, machine vendors are making use of long SIMD instruction registers that are able to process multiple data with one arithmetic operator in one clock cycle. SIMD register length is expected to double every four years. As a consequence, Particle-In-Cell (PIC) codes will have to achieve good vectorization to fully take advantage of these upcoming architectures. In this paper, we present a new algorithm that allows for efficient and portable SIMD vectorization of current/charge deposition routines that are, along with the field gathering routines, among the most time consuming parts of the PIC algorithm. Our new algorithm uses a particular data structure that takes into account memory alignment constraints and avoids gather/scat;ter instructions that can significantly affect vectorization performances on current CPUs. The new algorithm was successfully implemented in the 3D skeleton PIC code PICSAR and tested on Haswell Xeon processors (AVX2-256 bits wide data registers). Results show a factor of ×2 to ×2.5 speed-up in double precision for particle shape factor of orders 1–3. The new algorithm can be applied as is on future KNL (Knights Landing) architectures that will include AVX-512 instruction sets with 512 bits register lengths (8 doubles/16 singles). Program summary Program Title: vec_deposition Program Files doi:http://dx.doi.org/10.17632/nh77fv9k8c.1 Licensing provisions: BSD 3-Clause Programming language: Fortran 90 External routines/libraries: OpenMP > 4.0 Nature of problem: Exascale architectures will have many-core processors per node with long vector data registers capable of performing one single instruction on multiple data during one clock cycle. Data register lengths are expected to double every four years and this pushes for new portable solutions for efficiently vectorizing Particle-In-Cell codes on these future many-core architectures. One of the main hotspot routines of the PIC algorithm is the current/charge deposition for which there is no efficient and portable vector algorithm. Solution method: Here we provide an efficient and portable vector algorithm of current/charge deposition routines that uses a new data structure, which significantly reduces gather/scatter operations. Vectorization is controlled using OpenMP 4.0 compiler directives for vectorization which ensures portability across different architectures. Restrictions: Here we do not provide the full PIC algorithm with an executable but only vector routines for current/charge deposition. These scalar/vector routines can be used as library routines in your 3D Particle-In-Cell code. However, to get the best performances out of vector routines you have to satisfy the two following requirements: (1) Your code should implement particle tiling (as explained in the manuscript) to allow for maximized cache reuse and reduce memory accesses that can hinder vector performances. The routines can be used directly on each particle tile. (2) You should compile your code with a Fortran 90 compiler (e.g Intel, gnu or cray) and provide proper alignment flags and compiler alignment directives (more details in README file).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

SmartFuse: Reconfigurable Smart Switches to Accelerate Fused Collectives in HPC Applications

Communication switches have sometimes been augmented to process collectives (e.g., the IBM BlueGene project and the Mellanox SHArP switch). In this work, we find that there is a great acceleration opportunity through the further augmentation of switches to accelerate more complex functions that combine communication with computation. We consider three types of such functions. The first is fully-fused collectives built by fusing multiple existing collectives like Allreduce with Alltoall. The second is semi-fused collectives built by combining a collective with another computation. The third we refer to as higher-order collectives built by combining multiple computations and communications, such as to perform matrix-matrix multiply (PGEMM). In this work, we propose a framework called SmartFuse to accelerate fused collective functions. The core of SmartFuse is a reconfigurable smart switch to support these operations. The semi/fully fused collectives are implemented with a CGRAlike architecture, while higher-order collectives are implemented with a more specialized computational unit that can also schedule communication. Supporting our framework is software to evaluate and translate relevant parts of the input program, compile them into a control data flow graph, and then map this graph to the switch hardware. The proposed framework, once deployed, has the strong potential to accelerate existing HPC applications transparently by encapsulation within an MPI implementation. Experimental results show that this approach improves the performance of the PGEMM kernel, MINIFE, and AMG by, on average, 94%, 15%, and 13%, respectively.

Haghi, Pouya↗